The Thin Tweed Line
Navigation Bar Home Faculty Administration Students Trustees Government Tuition

Muḥammed ibn Mūsā al-Khwarizmi was born in the city of Bagdad Circa in 780 CE. Little to nothing is known about al-Khwarizmi’s private life, but his works in mathematics have been intact and have lived through the generations. His main work included breakthroughs in Algebra. Al-Khwarizmi’s full name is Abu Ja’far Muḥammed ibn Mūsā al-Khwarizmi, meaning he is Muhammad, the father of Jofar and the son of Musa from Khwarizm. During the reign of al-Ma’mum, the best scholars of the Islamic world were invited to the newly established Dar al-Hikma, otherwise known as the House of Wisdom. Al-Khwarizmi was selected to be the Chief astronomer and the head of the library at the House of Wisdom. This, along with Al-Khwarizmi’s desire for knowledge and scholarly abilities, gave him the opportunity and means to research and grow in his abilities as a scholar. Al-Khwarizmi’s contributions to mathematics have been an important factor to the growth and development of math departments in every university. (Swetz 26)

Al-Khwarizmi was said to be the “father of algebra.” This label was given to him and sticks with him because of the work and praise done for Al-Khwarizmi by the mathematicians that came after him. Along with the praise and admiration of mathematicians, the impact of his book on Europe led to the concrete thought that he was the “father of algebra.” Some scholars did not believe that Al-Khwarizmi was deserving of the title “father of algebra.” These scholars have shown that there were other forms of algebra before Al-Khwarizmi. One instance in which Al-Khwarizmi was not the first to discover algebra is when an ancient Babylonian problem was found in a cuneiform text. “What is the number, when added to its reciprocal, gives a known number?” (Al-Khalili 113-114). This translates into an equation which is similar to: Using this as an example shows that there is at least one individual who knew of algebra before Al-Khwarizmi. This also indicates that Al-Khwarizmi was not the first to understand the problem solving skills necessary for these unique problems. “Although Al-Khwarizmi was clearly building on the work of others before him, such as Diophantus and Brahmagupta, his was a much closer expression of the modern elementary algebra, and this is the reason he is sometimes referred to as ‘the father of algebra’” (Balchin 33). Al-Khwarizmi wrote a book called Kitab al-Jabr wa’l-Muqabala that later became the name of algebra (al-Jabr). Diophantus and Brahmagupta were two mathematicians that came before al-Khwarizmi.

It can be shown that Al-Khwarizmi built on the past work of Diophantus and Brahmagupta; but, it can also be deduced that Al-Khwarizmi’s work was not influenced by the classical Greek mathematics. “As Toomer notes in his article in the Dictionary of Scientific Biography, both Greek and Hindu algebra had advanced well beyond the elementary stage of Al-Khwarizmi’s work, and none of the known works in either culture shows much resemblance in presentation to Al-Khwarizmi’s work. As we have seen, his proofs of the methods of solution of quadratic equations are quite different from the proofs we find in Euclid’s Elements” (Waerden 12). This is to say that even though someone like Euclid had more advanced algebraic skills, it does not mean that Al-Khwarizmi was aware of them. Euclid is a Greek mathematician that wrote a book called Euclid’s Elements. Euclid’s works were more general than just algebra, but his thirteen-part book speaks about Euclid geometry.

It is essential to identify the meaning hidden behind the title of Kitab al-Jabr wa’l-Muqabala in order to understand how “algebra” earned its name. To break down the meaning of Kitab al-Jabr wa’l-Muqabala, the terms Jabr and Muqabala must be understood and defined. A treatise is a formal and systematic exposition in writing of the principles of a subject. Treatises are generally longer and more detailed than that of an essay. Usually, the meaning of Jabr in mathematic treatises is defined as adding equal terms to each side of an equation in order to eliminate negative terms. One meaning that is used less often is: multiplying both sides of an equation by one and the same number in order to eliminate fractions (Waerden 4). These are the basic levels of algebraic procedures that are still used today. On the flip side, the common meaning of muqabala is: reduction of positive terms by subtracting equal amounts from both sides of an equation. Al-Karaji, a fellow mathematician, uses this word in such a way that it also means “to equate”. The most literal translation and meaning ends up consisting of: comparing or posing opposite. Combining these two words gives us a more commonly understood meaning: performing algebraic equations or the science of algebra (Waerden 4). There is now a reasonable understanding as to why Al-Khwarizmi named his book in such a way. It is also reasonable to assume that the name algebra came from the title of this book.

Although a contemporary and closely related scholar of Al-Khwarizmi, al-Hajjaj ibn Yusuf, was translating Euclid’s Elements and Al-Khwarizmi should have known about it, there is no proof that he had any knowledge or connection to the works. “Some modern historians believe that Al-Khwarizmi’s use of geometric figures to supplement and justify his algebraic proofs suggests that he was familiar with the Elements and Euclid’s geometrical methods of solving problems” (Al-Khalili 117). It can neither be confirmed nor denied that al-Khwarizmi knew of Euclid’s geometrical methods. Although algebra was being used by other scholars on a much higher level, the information written in al-Khwarizmi’s book was a simplistic and elementary form of the algebra that made it easy for the masses to use.

Al-Khwarizmi was able to simplify and make algebra a basic and elementary concept because of the work he completed with Kushyar Gilani. Together, these two men introduced the “Hindu” numerals to Abbasids between CE825 and CE830. These “Hindu” numerals made it far easier to do mathematic equations as compared to the old use of the Greek numerals in equations that only few men knew how to solve. Along with the new set of numerals, al-Khwarizmi introduced zero as a possible lack of something and negative numbers were introduced as well. The “Hindu” numerals, zeroes, and negative numbers used in al-Khwarizmi’s book gained admiration from the other scholars. With this admiration comes the power of the word of mouth. With scholars and intellectual men speaking highly of this book and passing on copies, the book spread to other scholars and eventually made its way to Europe. Europe then took hold of this information and algebra became known to mass amounts of individuals, more than just the select few that knew it before.

Understanding the fact that there was knowledge before him and that his findings were not as widespread and elementary is essential to the reason al-Khwarizmi got the title. We can accurately call Al-Khwarizmi the father of algebra for bringing algebra to the world by founding algebra as an independent discipline and for introducing the methods of “reduction” and “balancing.” To give an accurate understanding of what algebra has done in present-day society, algebra has to make sense to other individuals. Algebra is the use of numbers in relation to statements of relations. Algebra utilizes letters and symbols to represent specific sets of numbers or values. Also, parts of algebra are linear functions and quadratic functions. Through the use of algebra, the world has had significant leaps forward.

There are further instances where algebra has helped shaped society. Algebra has made it possible to make accurate maps and mapping capabilities. This made each map more accurate and it was a stepping stone to the future of mapping and travel. One of the major outcomes of the introduction of algebra was the ability to use less materials and money to make better and more improved bridges and roads. Bridges had the ability to cross longer spans of water and they were made more durable and stronger. Algebra was used to help indicate where the bridge needed strong spots and where it could “free hang” instead of building a solid wall of stones that was called a bridge. With this, the amount of bridges and roads became more common. It was no longer necessary to be in the wealthiest area to have a bridge that made travel easier. Bridges were more widespread over the different rivers and bodies of water. Travel was highly impacted by this. Along with the bridges helping travel, algebra helped take some of the guess-work out of the measurements for sailing so that the correct amount of food, water, and other supplies were more accurate and precise. This new practical knowledge led to it being passed down so that it could be built upon and continued.

The Golden age of information for the Muslim people was a time for great leaps forward of knowledge. Not all the information was world changing. Although some knowledge on its own was not a game changer, it was a stepping stone for future intellectual figures to work with and turn into something of great importance or use. The want for this information to be passed from one generation to another led to the creation of universities as a way to educate the future intellects. Algebra became one of the great topics passed from one to another which made algebra a generally taught subject. From this knowledge of algebra and a more widespread use of it, algebra became a widely used and widely known skill.

The ability to use algebra in real life has been the greatest interpretation of algebra since al-Khwarizmi brought it into the sight of the masses. The use of real world algebra made it important for as many people as possible to know how to use algebra. The use of algebra skills were passed around to Universities, tutors, and even commoners. Universities have taught mathematics at the simplest form for as long as they have existed. The leaps forward have brought math into a multiclass system of anything from simple algebra to as complex a class as calculus III. Without the work of algebra from Al-Khwarizmi, there is no evidence that we would have the higher-level mathematic classes we do. On the other hand, there is also no proof that another scholar would not have figured it out by now. This later realization would have lead to later adaptations and in turn, made societies progress in mathematics: a thing to look forward to instead of back. Math has, and always will be, a growing subject that has so much more to expand on. Muḥammed ibn Mūsā al-Khwarizmi is one of the many scholars we have to thank for the level we are at today in regards to algebra and mathematics as a whole.

The development of math departments in universities has been greatly affected due to Al-Khwarizmi’s work on the subject of algebra. There are various individuals who have discovered far more complicated aspects of algebra far before Al-Khwarizmi began his exploration in algebra. However, Al-Khwarizmi earned the title “the father of algebra” by making algebra simplistic and making it so individuals can understand and use the subject. Thanks to Al-Khwarizmi, algebra is now easier to understand, allowing more individuals to further their education in mathematics. Without algebra, society would not be as sophisticated or developed as it is today. Buildings would not be as structurally sound, roads would not be as adequate, and bridges would not be able to span over vast bodies of water. If Al-Khwarizmi had not simplified algebra, algebra would not be a widely taught subject, especially in universities today.




Muḥammed ibn Mūsā al-Khwarizmi


Page Author: Logan R. Dearinger

Saturday, 11-Feb-2012 14:19


Al-Khalili, Jim. Pathfinders: The Golden Age of Arabic Science. London: Allen Lane, 2010. Print.

Al-Khwarizmi: The Father of Algebra." Web. 22 Jan. 2012.

Balchin, Jon. "Al-Khwārizmī." Science: 100 Scientists Who Changed the World. New York: Enchanted Lion, 2003. 32-33. Print

Brezina, Corona. Al-Khwarizmi: The Inventor of Algebra. New York: Rosen Pub. Group, 2006. Print.

Euclid, and Euclid. Euclid's Elements. London: Dent, 1933. Print.

Freely, John. Aladdin's Lamp: How Greek Science Came to Europe through the Islamic World. New York: Alfred A. Knopf, 2009. Print.

Jackson, Steve N. "The Thin Tweed Line: The Caliphate and the Muslim Renaissance." DHC 261. Black Hall Room 151, Ellensburg, WA. 24 Jan. 2012. Lecture.

Swetz, Frank J. "Al-Khwārizmī (ca. 800-847)." Learning Activities from the History of Mathematics. Portland, ME: J. Weston Walch, 1994. 26-27. Print.

Waerden, B.L. Van Der. A History of Algebra: From Al-Khwārizmī to Emmy Noether. Berlin: Springer-Verlag, 1985. Print.


Editorial Policy

Correspondence to the student authors of this website may be sent to this e-mail address. Make sure your subject includes the name of the author and the article you are referring to along with it's URL. Article copyright is held by their author.

Submissions of original new materials may be made electronically by PDF as long as significant authorship is by undergraduates enrolled in a non-profit educational institution. All materials are peer reviewed by a group of undergraduates.

Editorial articles, lecture presentations, and basic FAQs are marked as such on this website. These articles generally have open copyright and may be used in academic, non-profit settings as long as the author is given full attribution.

The Thin Tweed Line, ©2012 by Steve N. Jackson